Multiparty Cardinality Testing for Threshold Private Intersection

Abstract

Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than \(n-t\), where n is the size of each set and t is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold t and not on the sizes of the input sets. Current threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of threshold PSI is the former part.